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<li class="navelem"><a class="el" href="dir_d44c64559bbebec7f509842c48db8b23.html">include</a></li><li class="navelem"><a class="el" href="dir_d0c4ae63660968bf6b1c77a1e8aecf95.html">helib</a></li>  </ul>
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<div class="title">PGFFT.h</div>  </div>
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<a href="_p_g_f_f_t_8h.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno">    1</span>&#160; </div>
<div class="line"><a name="l00002"></a><span class="lineno">    2</span>&#160;<span class="comment">/**************************************************************************</span></div>
<div class="line"><a name="l00003"></a><span class="lineno">    3</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00004"></a><span class="lineno">    4</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00005"></a><span class="lineno">    5</span>&#160;<span class="comment">PGFFT: Pretty Good FFT (v1.8)</span></div>
<div class="line"><a name="l00006"></a><span class="lineno">    6</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00007"></a><span class="lineno">    7</span>&#160;<span class="comment">Copyright (C) 2019, Victor Shoup</span></div>
<div class="line"><a name="l00008"></a><span class="lineno">    8</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00009"></a><span class="lineno">    9</span>&#160;<span class="comment">See below for more details.</span></div>
<div class="line"><a name="l00010"></a><span class="lineno">   10</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00011"></a><span class="lineno">   11</span>&#160;<span class="comment">**************************************************************************/</span></div>
<div class="line"><a name="l00012"></a><span class="lineno">   12</span>&#160; </div>
<div class="line"><a name="l00013"></a><span class="lineno">   13</span>&#160;<span class="preprocessor">#if __cplusplus &lt;  201103L</span></div>
<div class="line"><a name="l00014"></a><span class="lineno">   14</span>&#160;<span class="preprocessor">#error &quot;C++11 required to compile PGFFT&quot;</span></div>
<div class="line"><a name="l00015"></a><span class="lineno">   15</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00016"></a><span class="lineno">   16</span>&#160; </div>
<div class="line"><a name="l00017"></a><span class="lineno">   17</span>&#160; </div>
<div class="line"><a name="l00018"></a><span class="lineno">   18</span>&#160; </div>
<div class="line"><a name="l00019"></a><span class="lineno">   19</span>&#160;<span class="preprocessor">#ifndef PGFFT_H</span></div>
<div class="line"><a name="l00020"></a><span class="lineno">   20</span>&#160;<span class="preprocessor">#define PGFFT_H</span></div>
<div class="line"><a name="l00021"></a><span class="lineno">   21</span>&#160; </div>
<div class="line"><a name="l00022"></a><span class="lineno">   22</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno">   23</span>&#160;<span class="preprocessor">#include &lt;complex&gt;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno">   24</span>&#160; </div>
<div class="line"><a name="l00025"></a><span class="lineno">   25</span>&#160;<span class="preprocessor">#pragma GCC diagnostic push</span></div>
<div class="line"><a name="l00026"></a><span class="lineno">   26</span>&#160;<span class="preprocessor">#pragma GCC diagnostic ignored &quot;-Wunused-parameter&quot;</span></div>
<div class="line"><a name="l00027"></a><span class="lineno">   27</span>&#160; </div>
<div class="line"><a name="l00028"></a><span class="lineno">   28</span>&#160;<span class="keyword">namespace </span><a class="code" href="namespacehelib.html">helib</a> {</div>
<div class="line"><a name="l00029"></a><span class="lineno">   29</span>&#160; </div>
<div class="line"><a name="l00030"></a><span class="lineno">   30</span>&#160;<span class="keyword">class </span>PGFFT {</div>
<div class="line"><a name="l00031"></a><span class="lineno">   31</span>&#160;<span class="keyword">public</span>:</div>
<div class="line"><a name="l00032"></a><span class="lineno">   32</span>&#160; </div>
<div class="line"><a name="l00033"></a><span class="lineno">   33</span>&#160;   <span class="comment">// initialize data strctures for n-point FFT</span></div>
<div class="line"><a name="l00034"></a><span class="lineno">   34</span>&#160;   <span class="comment">// REQUIREMENT: n &gt; 0</span></div>
<div class="line"><a name="l00035"></a><span class="lineno">   35</span>&#160;   <span class="keyword">explicit</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html#aeb1ed2dbd507c224c440cb2516431246">PGFFT</a>(<span class="keywordtype">long</span> n);</div>
<div class="line"><a name="l00036"></a><span class="lineno">   36</span>&#160; </div>
<div class="line"><a name="l00037"></a><span class="lineno">   37</span>&#160;   <span class="keywordtype">void</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a5d23bf5cdd6927d4398a74e7cd0ef9e0">apply</a>(<span class="keyword">const</span> std::complex&lt;double&gt;* src, std::complex&lt;double&gt;* dst) <span class="keyword">const</span>;</div>
<div class="line"><a name="l00038"></a><span class="lineno">   38</span>&#160;   <span class="comment">// Apply n-point FFT to src[0..n-1], storing result in dst[0..n-1].</span></div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html">   39</a></span>&#160;   <span class="comment">// That is,</span></div>
<div class="line"><a name="l00040"></a><span class="lineno">   40</span>&#160;   <span class="comment">//   dst[i] = \sum_{j=0}^{n-1} src[j] W^{ij}</span></div>
<div class="line"><a name="l00041"></a><span class="lineno">   41</span>&#160;   <span class="comment">// and where W is the nth root of unity polar(1, -2*pi/n).</span></div>
<div class="line"><a name="l00042"></a><span class="lineno">   42</span>&#160;   <span class="comment">// src and dst may be equal, but should not otherwise overlap</span></div>
<div class="line"><a name="l00043"></a><span class="lineno">   43</span>&#160; </div>
<div class="line"><a name="l00044"></a><span class="lineno">   44</span>&#160;   <span class="keywordtype">void</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a5d23bf5cdd6927d4398a74e7cd0ef9e0">apply</a>(std::complex&lt;double&gt;* v)<span class="keyword"> const </span>{ <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a5d23bf5cdd6927d4398a74e7cd0ef9e0">apply</a>(v, v); }</div>
<div class="line"><a name="l00045"></a><span class="lineno">   45</span>&#160;   <span class="comment">// same as apply(v, v)</span></div>
<div class="line"><a name="l00046"></a><span class="lineno">   46</span>&#160; </div>
<div class="line"><a name="l00047"></a><span class="lineno">   47</span>&#160;   <span class="comment">// Copy/move constructors/assignment ops deleted, as future implementations</span></div>
<div class="line"><a name="l00048"></a><span class="lineno">   48</span>&#160;   <span class="comment">// may not support them.</span></div>
<div class="line"><a name="l00049"></a><span class="lineno">   49</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#aeb1ed2dbd507c224c440cb2516431246">PGFFT</a>(<span class="keyword">const</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp;) = <span class="keyword">delete</span>;</div>
<div class="line"><a name="l00050"></a><span class="lineno">   50</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#aeb1ed2dbd507c224c440cb2516431246">PGFFT</a>(<a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp;&amp;) = <span class="keyword">delete</span>;</div>
<div class="line"><a name="l00051"></a><span class="lineno">   51</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp; <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a89a7a3fcbbb89fedfbd5fd5bcb6947e7">operator=</a>(<span class="keyword">const</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp;) = <span class="keyword">delete</span>;</div>
<div class="line"><a name="l00052"></a><span class="lineno">   52</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp; <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a89a7a3fcbbb89fedfbd5fd5bcb6947e7">operator=</a>(<a class="code" href="classhelib_1_1_p_g_f_f_t.html">PGFFT</a>&amp;&amp;) = <span class="keyword">delete</span>;</div>
<div class="line"><a name="l00053"></a><span class="lineno">   53</span>&#160; </div>
<div class="line"><a name="l00054"></a><span class="lineno">   54</span>&#160;   <span class="keyword">static</span> <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00055"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a5d23bf5cdd6927d4398a74e7cd0ef9e0">   55</a></span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a8500ecf9170170c438258992452a1395">simd_enabled</a>();</div>
<div class="line"><a name="l00056"></a><span class="lineno">   56</span>&#160; </div>
<div class="line"><a name="l00057"></a><span class="lineno">   57</span>&#160;   <span class="comment">// Define aligned vectors.</span></div>
<div class="line"><a name="l00058"></a><span class="lineno">   58</span>&#160;   <span class="comment">// This stuff should probably be private, but I&#39;m not sure</span></div>
<div class="line"><a name="l00059"></a><span class="lineno">   59</span>&#160;   <span class="comment">// of the rules for accessing these in the implementation file.</span></div>
<div class="line"><a name="l00060"></a><span class="lineno">   60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno">   61</span>&#160;   <span class="keyword">static</span> <span class="keywordtype">void</span> *</div>
<div class="line"><a name="l00062"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a7dad39eefa9f7b7ea3ce6d1e7d23c6d0">   62</a></span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a1bbcb197853ec5ab77a7fc7a053053fe">aligned_allocate</a>(std::size_t n, std::size_t nelts);</div>
<div class="line"><a name="l00063"></a><span class="lineno">   63</span>&#160; </div>
<div class="line"><a name="l00064"></a><span class="lineno">   64</span>&#160;   <span class="keyword">static</span> <span class="keywordtype">void</span></div>
<div class="line"><a name="l00065"></a><span class="lineno">   65</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#ae99a3f5a0c4480c07c2e4abfcb31505d">aligned_deallocate</a>(<span class="keywordtype">void</span> *p);</div>
<div class="line"><a name="l00066"></a><span class="lineno">   66</span>&#160; </div>
<div class="line"><a name="l00067"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a7f926a9eb6416a40ffb3d96feb602e33">   67</a></span>&#160;   <span class="keyword">template</span> &lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00068"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a87413b0718a6540db54b4023e3014382">   68</a></span>&#160;   <span class="keyword">class </span><a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html">aligned_allocator</a></div>
<div class="line"><a name="l00069"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a89a7a3fcbbb89fedfbd5fd5bcb6947e7">   69</a></span>&#160;   {</div>
<div class="line"><a name="l00070"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a1b24c5ab6a55ba3b49bd4cc362bff74f">   70</a></span>&#160;   <span class="keyword">public</span>:</div>
<div class="line"><a name="l00071"></a><span class="lineno">   71</span>&#160;       <span class="keyword">using</span> <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">value_type</a>    = T;</div>
<div class="line"><a name="l00072"></a><span class="lineno">   72</span>&#160; </div>
<div class="line"><a name="l00073"></a><span class="lineno">   73</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#af2340398126121c075252af309e8965e">aligned_allocator</a>() noexcept {}</div>
<div class="line"><a name="l00074"></a><span class="lineno">   74</span>&#160;       <span class="keyword">template</span> &lt;<span class="keyword">class</span> U&gt; <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#af2340398126121c075252af309e8965e">aligned_allocator</a>(aligned_allocator&lt;U&gt; <span class="keyword">const</span>&amp;) noexcept {}</div>
<div class="line"><a name="l00075"></a><span class="lineno">   75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno">   76</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">value_type</a>*</div>
<div class="line"><a name="l00077"></a><span class="lineno">   77</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a8d2d325eb8ea605a2155a02282c94d7b">allocate</a>(std::size_t n)</div>
<div class="line"><a name="l00078"></a><span class="lineno">   78</span>&#160;       {</div>
<div class="line"><a name="l00079"></a><span class="lineno">   79</span>&#160;           <span class="keywordtype">void</span> *p = <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a1bbcb197853ec5ab77a7fc7a053053fe">aligned_allocate</a>(n, <span class="keyword">sizeof</span>(T));</div>
<div class="line"><a name="l00080"></a><span class="lineno">   80</span>&#160;           <span class="keywordflow">if</span> (p) {</div>
<div class="line"><a name="l00081"></a><span class="lineno">   81</span>&#160;          <span class="keywordflow">return</span> <span class="keyword">static_cast&lt;</span><a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">value_type</a>*<span class="keyword">&gt;</span>(p);</div>
<div class="line"><a name="l00082"></a><span class="lineno">   82</span>&#160;           }</div>
<div class="line"><a name="l00083"></a><span class="lineno">   83</span>&#160; </div>
<div class="line"><a name="l00084"></a><span class="lineno">   84</span>&#160;           <span class="keywordflow">throw</span> std::bad_alloc();</div>
<div class="line"><a name="l00085"></a><span class="lineno">   85</span>&#160;       }</div>
<div class="line"><a name="l00086"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html">   86</a></span>&#160; </div>
<div class="line"><a name="l00087"></a><span class="lineno">   87</span>&#160;       <span class="keywordtype">void</span></div>
<div class="line"><a name="l00088"></a><span class="lineno">   88</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a9c2bb38e0a4e294bcf192a472dea42f0">deallocate</a>(<a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">value_type</a>* p, std::size_t) noexcept</div>
<div class="line"><a name="l00089"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">   89</a></span>&#160;       {</div>
<div class="line"><a name="l00090"></a><span class="lineno">   90</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t.html#ae99a3f5a0c4480c07c2e4abfcb31505d">aligned_deallocate</a>(p);</div>
<div class="line"><a name="l00091"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#af2340398126121c075252af309e8965e">   91</a></span>&#160;       }</div>
<div class="line"><a name="l00092"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a48a62f34e8dc44b029572b833d4c935a">   92</a></span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno">   93</span>&#160;       <span class="keyword">template</span> &lt;<span class="keyword">class</span> U&gt;</div>
<div class="line"><a name="l00094"></a><span class="lineno">   94</span>&#160;       <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00095"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a8d2d325eb8ea605a2155a02282c94d7b">   95</a></span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a22f91140ca6bd4c3717b3e7d0d2a766b">operator==</a>(<a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html">aligned_allocator&lt;U&gt;</a> <span class="keyword">const</span>&amp;) noexcept</div>
<div class="line"><a name="l00096"></a><span class="lineno">   96</span>&#160;       {</div>
<div class="line"><a name="l00097"></a><span class="lineno">   97</span>&#160;       <span class="keywordflow">return</span> <span class="keyword">true</span>;</div>
<div class="line"><a name="l00098"></a><span class="lineno">   98</span>&#160;       }</div>
<div class="line"><a name="l00099"></a><span class="lineno">   99</span>&#160; </div>
<div class="line"><a name="l00100"></a><span class="lineno">  100</span>&#160;       <span class="keyword">template</span> &lt;<span class="keyword">class</span> U&gt;</div>
<div class="line"><a name="l00101"></a><span class="lineno">  101</span>&#160;       <span class="keywordtype">bool</span></div>
<div class="line"><a name="l00102"></a><span class="lineno">  102</span>&#160;       <a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a7bd2e92911869bc27193071787a7da6f">operator!=</a>(<a class="code" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html">aligned_allocator&lt;U&gt;</a> <span class="keyword">const</span>&amp; y) noexcept</div>
<div class="line"><a name="l00103"></a><span class="lineno">  103</span>&#160;       {</div>
<div class="line"><a name="l00104"></a><span class="lineno">  104</span>&#160;       <span class="keywordflow">return</span> <span class="keyword">false</span>;</div>
<div class="line"><a name="l00105"></a><span class="lineno">  105</span>&#160;       }</div>
<div class="line"><a name="l00106"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a9c2bb38e0a4e294bcf192a472dea42f0">  106</a></span>&#160;   };</div>
<div class="line"><a name="l00107"></a><span class="lineno">  107</span>&#160; </div>
<div class="line"><a name="l00108"></a><span class="lineno">  108</span>&#160;   <span class="keyword">template</span>&lt;<span class="keyword">class</span> T&gt;</div>
<div class="line"><a name="l00109"></a><span class="lineno">  109</span>&#160;   <span class="keyword">using</span> <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a618bb04e868985f8159d8063829f1f88">aligned_vector</a>= std::vector&lt;T,aligned_allocator&lt;T&gt;&gt;;</div>
<div class="line"><a name="l00110"></a><span class="lineno">  110</span>&#160; </div>
<div class="line"><a name="l00111"></a><span class="lineno">  111</span>&#160; </div>
<div class="line"><a name="l00112"></a><span class="lineno">  112</span>&#160; </div>
<div class="line"><a name="l00113"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a22f91140ca6bd4c3717b3e7d0d2a766b">  113</a></span>&#160;<span class="keyword">private</span>:</div>
<div class="line"><a name="l00114"></a><span class="lineno">  114</span>&#160; </div>
<div class="line"><a name="l00115"></a><span class="lineno">  115</span>&#160;   <span class="keywordtype">long</span> n;</div>
<div class="line"><a name="l00116"></a><span class="lineno">  116</span>&#160;   <span class="keywordtype">long</span> k;</div>
<div class="line"><a name="l00117"></a><span class="lineno">  117</span>&#160; </div>
<div class="line"><a name="l00118"></a><span class="lineno">  118</span>&#160;   <span class="keywordtype">long</span> strategy;</div>
<div class="line"><a name="l00119"></a><span class="lineno">  119</span>&#160; </div>
<div class="line"><a name="l00120"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a7bd2e92911869bc27193071787a7da6f">  120</a></span>&#160;   <span class="comment">// holds all of the twiddle factors</span></div>
<div class="line"><a name="l00121"></a><span class="lineno">  121</span>&#160;   std::vector&lt;aligned_vector&lt;std::complex&lt;double&gt;&gt;&gt; tab;</div>
<div class="line"><a name="l00122"></a><span class="lineno">  122</span>&#160; </div>
<div class="line"><a name="l00123"></a><span class="lineno">  123</span>&#160;   <span class="comment">// additional data structures needed for Bluestein</span></div>
<div class="line"><a name="l00124"></a><span class="lineno">  124</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a618bb04e868985f8159d8063829f1f88">aligned_vector&lt;std::complex&lt;double&gt;</a>&gt; powers;</div>
<div class="line"><a name="l00125"></a><span class="lineno">  125</span>&#160;   <a class="code" href="classhelib_1_1_p_g_f_f_t.html#a618bb04e868985f8159d8063829f1f88">aligned_vector&lt;std::complex&lt;double&gt;</a>&gt; Rb;</div>
<div class="line"><a name="l00126"></a><span class="lineno">  126</span>&#160; </div>
<div class="line"><a name="l00127"></a><span class="lineno"><a class="line" href="classhelib_1_1_p_g_f_f_t.html#a618bb04e868985f8159d8063829f1f88">  127</a></span>&#160;   <span class="comment">// additonal data structures needed for 2^k-point FFT</span></div>
<div class="line"><a name="l00128"></a><span class="lineno">  128</span>&#160;   std::vector&lt;long&gt; rev, rev1;</div>
<div class="line"><a name="l00129"></a><span class="lineno">  129</span>&#160; </div>
<div class="line"><a name="l00130"></a><span class="lineno">  130</span>&#160; </div>
<div class="line"><a name="l00131"></a><span class="lineno">  131</span>&#160; </div>
<div class="line"><a name="l00132"></a><span class="lineno">  132</span>&#160; </div>
<div class="line"><a name="l00133"></a><span class="lineno">  133</span>&#160; </div>
<div class="line"><a name="l00134"></a><span class="lineno">  134</span>&#160;};</div>
<div class="line"><a name="l00135"></a><span class="lineno">  135</span>&#160; </div>
<div class="line"><a name="l00136"></a><span class="lineno">  136</span>&#160;}</div>
<div class="line"><a name="l00137"></a><span class="lineno">  137</span>&#160; </div>
<div class="line"><a name="l00138"></a><span class="lineno">  138</span>&#160;<span class="preprocessor">#endif</span></div>
<div class="line"><a name="l00139"></a><span class="lineno">  139</span>&#160; </div>
<div class="line"><a name="l00140"></a><span class="lineno">  140</span>&#160;<span class="comment">/**************************************************************************</span></div>
<div class="line"><a name="l00141"></a><span class="lineno">  141</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00142"></a><span class="lineno">  142</span>&#160;<span class="comment">PGFFT: Pretty Good FFT (v1.8)</span></div>
<div class="line"><a name="l00143"></a><span class="lineno">  143</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00144"></a><span class="lineno">  144</span>&#160;<span class="comment">Copyright (C) 2019, Victor Shoup</span></div>
<div class="line"><a name="l00145"></a><span class="lineno">  145</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00146"></a><span class="lineno">  146</span>&#160;<span class="comment">All rights reserved.</span></div>
<div class="line"><a name="l00147"></a><span class="lineno">  147</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00148"></a><span class="lineno">  148</span>&#160;<span class="comment">Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00149"></a><span class="lineno">  149</span>&#160;<span class="comment">modification, are permitted provided that the following conditions are met:</span></div>
<div class="line"><a name="l00150"></a><span class="lineno">  150</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00151"></a><span class="lineno">  151</span>&#160;<span class="comment">* Redistributions of source code must retain the above copyright notice, this</span></div>
<div class="line"><a name="l00152"></a><span class="lineno">  152</span>&#160;<span class="comment">  list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00153"></a><span class="lineno">  153</span>&#160;<span class="comment">* Redistributions in binary form must reproduce the above copyright notice,</span></div>
<div class="line"><a name="l00154"></a><span class="lineno">  154</span>&#160;<span class="comment">  this list of conditions and the following disclaimer in the documentation</span></div>
<div class="line"><a name="l00155"></a><span class="lineno">  155</span>&#160;<span class="comment">  and/or other materials provided with the distribution.</span></div>
<div class="line"><a name="l00156"></a><span class="lineno">  156</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00157"></a><span class="lineno">  157</span>&#160;<span class="comment">THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS &quot;AS IS&quot;</span></div>
<div class="line"><a name="l00158"></a><span class="lineno">  158</span>&#160;<span class="comment">AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span></div>
<div class="line"><a name="l00159"></a><span class="lineno">  159</span>&#160;<span class="comment">IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE</span></div>
<div class="line"><a name="l00160"></a><span class="lineno">  160</span>&#160;<span class="comment">DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE</span></div>
<div class="line"><a name="l00161"></a><span class="lineno">  161</span>&#160;<span class="comment">FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL</span></div>
<div class="line"><a name="l00162"></a><span class="lineno">  162</span>&#160;<span class="comment">DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR</span></div>
<div class="line"><a name="l00163"></a><span class="lineno">  163</span>&#160;<span class="comment">SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER</span></div>
<div class="line"><a name="l00164"></a><span class="lineno">  164</span>&#160;<span class="comment">CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,</span></div>
<div class="line"><a name="l00165"></a><span class="lineno">  165</span>&#160;<span class="comment">OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE</span></div>
<div class="line"><a name="l00166"></a><span class="lineno">  166</span>&#160;<span class="comment">OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00167"></a><span class="lineno">  167</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00168"></a><span class="lineno">  168</span>&#160;<span class="comment">****************************************************************************</span></div>
<div class="line"><a name="l00169"></a><span class="lineno">  169</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00170"></a><span class="lineno">  170</span>&#160;<span class="comment">The logic of this code is derived from code originally developed by David Harvey,</span></div>
<div class="line"><a name="l00171"></a><span class="lineno">  171</span>&#160;<span class="comment">even though the code itself has been essentially rewritten from scratch.</span></div>
<div class="line"><a name="l00172"></a><span class="lineno">  172</span>&#160;<span class="comment">Here is David Harvey&#39;s original copyright notice.</span></div>
<div class="line"><a name="l00173"></a><span class="lineno">  173</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00174"></a><span class="lineno">  174</span>&#160;<span class="comment">fft62: a library for number-theoretic transforms</span></div>
<div class="line"><a name="l00175"></a><span class="lineno">  175</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00176"></a><span class="lineno">  176</span>&#160;<span class="comment">Copyright (C) 2013, David Harvey</span></div>
<div class="line"><a name="l00177"></a><span class="lineno">  177</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00178"></a><span class="lineno">  178</span>&#160;<span class="comment">All rights reserved.</span></div>
<div class="line"><a name="l00179"></a><span class="lineno">  179</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00180"></a><span class="lineno">  180</span>&#160;<span class="comment">Redistribution and use in source and binary forms, with or without</span></div>
<div class="line"><a name="l00181"></a><span class="lineno">  181</span>&#160;<span class="comment">modification, are permitted provided that the following conditions are met:</span></div>
<div class="line"><a name="l00182"></a><span class="lineno">  182</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00183"></a><span class="lineno">  183</span>&#160;<span class="comment">* Redistributions of source code must retain the above copyright notice, this</span></div>
<div class="line"><a name="l00184"></a><span class="lineno">  184</span>&#160;<span class="comment">  list of conditions and the following disclaimer.</span></div>
<div class="line"><a name="l00185"></a><span class="lineno">  185</span>&#160;<span class="comment">* Redistributions in binary form must reproduce the above copyright notice,</span></div>
<div class="line"><a name="l00186"></a><span class="lineno">  186</span>&#160;<span class="comment">  this list of conditions and the following disclaimer in the documentation</span></div>
<div class="line"><a name="l00187"></a><span class="lineno">  187</span>&#160;<span class="comment">  and/or other materials provided with the distribution.</span></div>
<div class="line"><a name="l00188"></a><span class="lineno">  188</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00189"></a><span class="lineno">  189</span>&#160;<span class="comment">THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS &quot;AS IS&quot;</span></div>
<div class="line"><a name="l00190"></a><span class="lineno">  190</span>&#160;<span class="comment">AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE</span></div>
<div class="line"><a name="l00191"></a><span class="lineno">  191</span>&#160;<span class="comment">IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE</span></div>
<div class="line"><a name="l00192"></a><span class="lineno">  192</span>&#160;<span class="comment">DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE</span></div>
<div class="line"><a name="l00193"></a><span class="lineno">  193</span>&#160;<span class="comment">FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL</span></div>
<div class="line"><a name="l00194"></a><span class="lineno">  194</span>&#160;<span class="comment">DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR</span></div>
<div class="line"><a name="l00195"></a><span class="lineno">  195</span>&#160;<span class="comment">SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER</span></div>
<div class="line"><a name="l00196"></a><span class="lineno">  196</span>&#160;<span class="comment">CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,</span></div>
<div class="line"><a name="l00197"></a><span class="lineno">  197</span>&#160;<span class="comment">OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE</span></div>
<div class="line"><a name="l00198"></a><span class="lineno">  198</span>&#160;<span class="comment">OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.</span></div>
<div class="line"><a name="l00199"></a><span class="lineno">  199</span>&#160;<span class="comment"></span> </div>
<div class="line"><a name="l00200"></a><span class="lineno">  200</span>&#160;<span class="comment">****************************************************************************/</span></div>
<div class="line"><a name="l00201"></a><span class="lineno">  201</span>&#160; </div>
<div class="line"><a name="l00202"></a><span class="lineno">  202</span>&#160;<span class="preprocessor">#pragma GCC diagnostic pop</span></div>
</div><!-- fragment --></div><!-- contents -->
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_a5d23bf5cdd6927d4398a74e7cd0ef9e0"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#a5d23bf5cdd6927d4398a74e7cd0ef9e0">helib::PGFFT::apply</a></div><div class="ttdeci">void apply(const std::complex&lt; double &gt; *src, std::complex&lt; double &gt; *dst) const</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_aeb1ed2dbd507c224c440cb2516431246"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#aeb1ed2dbd507c224c440cb2516431246">helib::PGFFT::PGFFT</a></div><div class="ttdeci">PGFFT(long n)</div><div class="ttdef"><b>Definition:</b> PGFFT.cpp:1520</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_aef7385525e57d83cecb045c9eab57a23"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#aef7385525e57d83cecb045c9eab57a23">helib::PGFFT::aligned_allocator::value_type</a></div><div class="ttdeci">T value_type</div><div class="ttdef"><b>Definition:</b> PGFFT.h:89</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_a8d2d325eb8ea605a2155a02282c94d7b"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a8d2d325eb8ea605a2155a02282c94d7b">helib::PGFFT::aligned_allocator::allocate</a></div><div class="ttdeci">value_type * allocate(std::size_t n)</div><div class="ttdef"><b>Definition:</b> PGFFT.h:95</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_af2340398126121c075252af309e8965e"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#af2340398126121c075252af309e8965e">helib::PGFFT::aligned_allocator::aligned_allocator</a></div><div class="ttdeci">aligned_allocator() noexcept</div><div class="ttdef"><b>Definition:</b> PGFFT.h:91</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html">helib::PGFFT</a></div><div class="ttdef"><b>Definition:</b> PGFFT.h:39</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_a8500ecf9170170c438258992452a1395"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#a8500ecf9170170c438258992452a1395">helib::PGFFT::simd_enabled</a></div><div class="ttdeci">static bool simd_enabled()</div><div class="ttdef"><b>Definition:</b> PGFFT.cpp:82</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_a1bbcb197853ec5ab77a7fc7a053053fe"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#a1bbcb197853ec5ab77a7fc7a053053fe">helib::PGFFT::aligned_allocate</a></div><div class="ttdeci">static void * aligned_allocate(std::size_t n, std::size_t nelts)</div><div class="ttdef"><b>Definition:</b> PGFFT.cpp:168</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_a7bd2e92911869bc27193071787a7da6f"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a7bd2e92911869bc27193071787a7da6f">helib::PGFFT::aligned_allocator::operator!=</a></div><div class="ttdeci">bool operator!=(aligned_allocator&lt; U &gt; const &amp;y) noexcept</div><div class="ttdef"><b>Definition:</b> PGFFT.h:120</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html">helib::PGFFT::aligned_allocator</a></div><div class="ttdef"><b>Definition:</b> PGFFT.h:87</div></div>
<div class="ttc" id="anamespacehelib_html"><div class="ttname"><a href="namespacehelib.html">helib</a></div><div class="ttdef"><b>Definition:</b> apiAttributes.h:21</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_a89a7a3fcbbb89fedfbd5fd5bcb6947e7"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#a89a7a3fcbbb89fedfbd5fd5bcb6947e7">helib::PGFFT::operator=</a></div><div class="ttdeci">PGFFT &amp; operator=(const PGFFT &amp;)=delete</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_a618bb04e868985f8159d8063829f1f88"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#a618bb04e868985f8159d8063829f1f88">helib::PGFFT::aligned_vector</a></div><div class="ttdeci">std::vector&lt; T, aligned_allocator&lt; T &gt; &gt; aligned_vector</div><div class="ttdef"><b>Definition:</b> PGFFT.h:127</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_a22f91140ca6bd4c3717b3e7d0d2a766b"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a22f91140ca6bd4c3717b3e7d0d2a766b">helib::PGFFT::aligned_allocator::operator==</a></div><div class="ttdeci">bool operator==(aligned_allocator&lt; U &gt; const &amp;) noexcept</div><div class="ttdef"><b>Definition:</b> PGFFT.h:113</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_html_ae99a3f5a0c4480c07c2e4abfcb31505d"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t.html#ae99a3f5a0c4480c07c2e4abfcb31505d">helib::PGFFT::aligned_deallocate</a></div><div class="ttdeci">static void aligned_deallocate(void *p)</div><div class="ttdef"><b>Definition:</b> PGFFT.cpp:176</div></div>
<div class="ttc" id="aclasshelib_1_1_p_g_f_f_t_1_1aligned__allocator_html_a9c2bb38e0a4e294bcf192a472dea42f0"><div class="ttname"><a href="classhelib_1_1_p_g_f_f_t_1_1aligned__allocator.html#a9c2bb38e0a4e294bcf192a472dea42f0">helib::PGFFT::aligned_allocator::deallocate</a></div><div class="ttdeci">void deallocate(value_type *p, std::size_t) noexcept</div><div class="ttdef"><b>Definition:</b> PGFFT.h:106</div></div>
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